Problem: Multiply and simplify the following complex numbers: $({-4-4i}) \cdot ({-5-3i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-4-4i}) \cdot ({-5-3i}) = $ $ ({-4} \cdot {-5}) + ({-4} \cdot {-3i}) + ({-4i} \cdot {-5}) + ({-4i} \cdot {-3i}) $ Then simplify the terms: $ (20) + (12i) + (20i) + (12i^2) $ Imaginary unit multiples can be grouped together. $ 20 + (12 + 20)i + 12 i^2 $ After we plug in $i^2 = -1$, the result becomes $ 20 + (12 + 20)i - 12 $ The result is simplified: $ (20 - 12) + (32i) = 8+32i $